The present invention relates to Strap Assemblies Tonneau Covers, particularly roll-up covers having a flexible cover and an apparatus for attachment of the flexible cover to a cargo box of a pick up truck. The attachment apparatus includes a support frame for securing the flexible cover to the cargo box of a pick-up truck and mechanisms for securing the flexible cover in a rolled-up configuration when the flexible cover is not in use over the top of the cargo box. In preferred embodiments strap assemblies including straps and strap brackets are provided to secure the flexible Tonneau Cover.